On approximate implicit Taylor methods for ordinary differential equations
| Autor: | Antonio Baeza, David Zorío, Pep Mulet, Raimund Bürger, M. C. Martí |
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| Rok vydání: | 2020 |
| Předmět: |
Discretization
Applied Mathematics MathematicsofComputing_NUMERICALANALYSIS Ode 010103 numerical & computational mathematics Function (mathematics) 01 natural sciences 010101 applied mathematics Computational Mathematics Ordinary differential equation Scheme (mathematics) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Order (group theory) Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Computational and Applied Mathematics. 39 |
| ISSN: | 1807-0302 2238-3603 |
| Popis: | An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a method that requires less evaluations of the function that defines the ODE and its derivatives than the usual version. On the other hand, an efficient numerical solution of the equation that arises from the discretization by means of Newton’s method is introduced for an implicit scheme of any order. Numerical experiments illustrate that the resulting algorithm is simpler to implement and has better performance than its exact counterpart. |
| Databáze: | OpenAIRE |
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